I guess you are referring to this part: "A very intriguing, and perhaps unintuitive property of the algorithm proposed is that with increasing bitcoin difficul

I guess you are referring to this part: "A very intriguing, and perhaps unintuitive property of the algorithm proposed is that with increasing bitcoin difficulty, or equally lower target, the search could become more efficient, at least in theory. This is because we can assume more about the structure of a valid hash -- a lower target means more leading zeros which are assumed to be zero in the SAT-based algorithm." This is actually pretty misleading. There might be fewer variables, but that's irrelevant. Yes, there are actually fewer variables in the actual file you feed to the SAT solver because you can assume they are 0 and propagate that to the other constraints involving those variables. But think about it -- you're only going to get rid of a couple of hundred variables at most, in a problem with ~250,000 variables. So you're only really reducing the full search space by an incredibly small percentage. In practice, the running time of the SAT solver increases exponentially with the number of zeros you assume in the hash, just like it does for a regular brute force trying all combinations of inputs. The conclusion I draw from this is that not all variables contribute equally to the difficulty of a problem (for a SAT solver). This is actually why SAT solvers can be efficient for some problems in the first place, even for problems with hundreds of thousands of variables; the SAT solver (a smart brute force, as opposed to a naive brute force) is able to exploit the fact that many problems you feed to it are not intrinsically hard.